Question: Express your answer as a mixed number simplified to lowest terms. $6\dfrac{1}{7}-2\dfrac{2}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {6\dfrac{3}{21}}-{2\dfrac{14}{21}}$ Convert ${6\dfrac{3}{21}}$ to ${5 + \dfrac{21}{21} + \dfrac{3}{21}}$ So the problem becomes: ${5\dfrac{24}{21}}-{2\dfrac{14}{21}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{24}{21}} - {2} - {\dfrac{14}{21}}$ Bring the whole numbers together and the fractions together: $= {5} - {2} + {\dfrac{24}{21}} - {\dfrac{14}{21}}$ Subtract the whole numbers: $=3 + {\dfrac{24}{21}} - {\dfrac{14}{21}}$ Subtract the fractions: $= 3+\dfrac{10}{21}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{10}{21}$